How to define a tensor space

Lily
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4 years 1 month ago #2869 by Lily

How to define a tensor space was created by Lily

Hi,

I am trying to define a symmetric stress tensor. I wonder if there is any sentence like "TensorL2(mesh, order=1, sym=symmtry) ", and if there is any example that uses tensor space?

Thanks in advance.

mneunteufel
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4 years 1 month ago #2870 by mneunteufel

Replied by mneunteufel on topic How to define a tensor space

Hi Lily,

currently there is no "TensorL2" FESpace directly available in NGSolve. You can use copies of L2 to construct a symmetric tensor space. E.g. in 2D

Code:

fesL2 = L2(mesh, order=1)
MatrixL2 = FESpace( [fesL2,fesL2,fesL2] )
(uxx,uxy,uyy),(vxx,vxy,vyy) = MatrixL2.TnT()

um = CoefficientFunction( (uxx, uxy,
                           uxy, uyy), dims=(2,2))
vm = CoefficientFunction( (vxx, vxy,
                           vxy, vyy), dims=(2,2))

...

gf = GridFunction(MatrixL2)
gfm = CoefficientFunction( (gf.components[0],gf.components[1],
                            gf.components[1],gf.components[2]), dims=(2,2) )
Draw(gfm,mesh,"gfm")

Attached you'll find a minimal example where a non-symmetric matrix gets projected.

There are matrix-valued spaces in NGSolve: HDivDiv, HCurlCurl, HCurlDiv (the first two are symmetric, the latter is not). The HDivDiv space is used e.g. in the Hellan-Herrmann-Johnson method for forth-order problems.

Best
Michael

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The following user(s) said Thank You: Manuel Sanchez

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